[{"year":"2026","status":"public","intvolume":"        12","issue":"12","volume":12,"OA_type":"gold","article_processing_charge":"No","quality_controlled":"1","_id":"21583","type":"journal_article","title":"Experimental observation of energy-band Riemann surface","abstract":[{"text":"Non-Hermiticity naturally arises in physical systems that exchange energy with their environment. The presence of non-Hermiticity leads to many topological physics phenomena and device applications. In the non-Hermitian energy band theory, the foundation of these physics and applications, both energies and wave vectors take complex values. The energy bands thus become a Riemann surface, and such an energy-band Riemann surface underlies all important signatures of non-Hermitian topology. Despite a long history and recent theoretical interests, the energy-band Riemann surface has not been experimentally studied. Here, we provide a photonic observation of the energy-band Riemann surface of a non-Hermitian system. This is achieved by a tunable imaginary gauge transformation in photonic synthetic frequency dimensions. From measured topologies of the Riemann surface, we reveal the complex-energy winding, the open-boundary-condition spectrum, the generalized Brillouin zone, and the branch points. Our findings demonstrate a unified framework in the studies of diverse effects in non-Hermitian topological physics through an experimental observation of energy-band Riemann surfaces.","lang":"eng"}],"doi":"10.1126/sciadv.aec8239","article_type":"original","OA_place":"publisher","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1126/sciadv.aec8239"}],"oa":1,"month":"03","author":[{"last_name":"Cheng","full_name":"Cheng, Dali","first_name":"Dali"},{"last_name":"Wang","full_name":"Wang, Heming","first_name":"Heming"},{"first_name":"Janet","last_name":"Zhong","full_name":"Zhong, Janet"},{"first_name":"Eran","full_name":"Lustig, Eran","last_name":"Lustig"},{"id":"e2e68fc9-6505-11ef-a541-eb4e72cc3e82","last_name":"Roques-Carmes","full_name":"Roques-Carmes, Charles","first_name":"Charles"},{"first_name":"Shanhui","last_name":"Fan","full_name":"Fan, Shanhui"}],"DOAJ_listed":"1","date_updated":"2026-04-27T10:01:35Z","oa_version":"Published Version","date_published":"2026-03-18T00:00:00Z","external_id":{"arxiv":["2510.08819"]},"article_number":"eaec8239","publication_identifier":{"issn":["2375-2548"]},"arxiv":1,"day":"18","scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publisher":"American Association for the Advancement of Science","date_created":"2026-03-30T12:22:48Z","publication":"Science Advances","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Cheng, D., Wang, H., Zhong, J., Lustig, E., Roques-Carmes, C., &#38; Fan, S. (2026). Experimental observation of energy-band Riemann surface. <i>Science Advances</i>. American Association for the Advancement of Science. <a href=\"https://doi.org/10.1126/sciadv.aec8239\">https://doi.org/10.1126/sciadv.aec8239</a>","ista":"Cheng D, Wang H, Zhong J, Lustig E, Roques-Carmes C, Fan S. 2026. Experimental observation of energy-band Riemann surface. Science Advances. 12(12), eaec8239.","chicago":"Cheng, Dali, Heming Wang, Janet Zhong, Eran Lustig, Charles Roques-Carmes, and Shanhui Fan. “Experimental Observation of Energy-Band Riemann Surface.” <i>Science Advances</i>. American Association for the Advancement of Science, 2026. <a href=\"https://doi.org/10.1126/sciadv.aec8239\">https://doi.org/10.1126/sciadv.aec8239</a>.","ama":"Cheng D, Wang H, Zhong J, Lustig E, Roques-Carmes C, Fan S. Experimental observation of energy-band Riemann surface. <i>Science Advances</i>. 2026;12(12). doi:<a href=\"https://doi.org/10.1126/sciadv.aec8239\">10.1126/sciadv.aec8239</a>","short":"D. Cheng, H. Wang, J. Zhong, E. Lustig, C. Roques-Carmes, S. Fan, Science Advances 12 (2026).","ieee":"D. Cheng, H. Wang, J. Zhong, E. Lustig, C. Roques-Carmes, and S. Fan, “Experimental observation of energy-band Riemann surface,” <i>Science Advances</i>, vol. 12, no. 12. American Association for the Advancement of Science, 2026.","mla":"Cheng, Dali, et al. “Experimental Observation of Energy-Band Riemann Surface.” <i>Science Advances</i>, vol. 12, no. 12, eaec8239, American Association for the Advancement of Science, 2026, doi:<a href=\"https://doi.org/10.1126/sciadv.aec8239\">10.1126/sciadv.aec8239</a>."}}]